Question
$\frac{2\text{x}-1}{3}-\frac{6\text{x}-2}{5}=\frac{1}{3}$
✓
Answer
$\frac{2\text{x}-1}{3}-\frac{6\text{x}-2}{5}=\frac{1}{3}$
$=\frac{5(2\text{x}-1)-3(6\text{x}-2)}{15}=\frac{1}{3}$
$=\frac{10\text{x}-5-18\text{x}+6}{15}=\frac{1}{3}$ (L.C.M. of 3, 5 = 15)
$=\frac{-8\text{x}+1}{15}=\frac{1}{3}$
$\Rightarrow(-8\text{x}+1)\times3=1\times15$ (By cross multiplication)
$\Rightarrow$ Dividing by 3
$\frac{(-8\text{x}+1)\times3}{3}=\frac{1\times15}{3}$
$\Rightarrow-8\text{x}+1=5$
Subtracting 1 from both side,
$-8\text{x}+1-1=5-1$
$\Rightarrow-8\text{x}=4$
Dividing by -8,
$\frac{-8\text{x}}{-8}=\frac{4}{-8}$
$\Rightarrow\text{x}=\frac{1}{-2}$
$\therefore\text{x}=\frac{-1}{2}$
Verification:
$\text{L.H.S.}=\frac{2\text{x}-1}{3}-\frac{6\text{x}-2}{5}$
$=\frac{2\Big(\frac{-1}{2}\Big)-1}{3}-\frac{6\Big(\frac{-1}{2}\Big)-2}{5}$
$=\frac{-1-1}{3}-\frac{-3-2}{5}$
$=\frac{-2}{3}-\frac{-5}{5}=\frac{-2}{3}+1$
$=\frac{1}{3}=\text{R.H.S.}$
$=\frac{5(2\text{x}-1)-3(6\text{x}-2)}{15}=\frac{1}{3}$
$=\frac{10\text{x}-5-18\text{x}+6}{15}=\frac{1}{3}$ (L.C.M. of 3, 5 = 15)
$=\frac{-8\text{x}+1}{15}=\frac{1}{3}$
$\Rightarrow(-8\text{x}+1)\times3=1\times15$ (By cross multiplication)
$\Rightarrow$ Dividing by 3
$\frac{(-8\text{x}+1)\times3}{3}=\frac{1\times15}{3}$
$\Rightarrow-8\text{x}+1=5$
Subtracting 1 from both side,
$-8\text{x}+1-1=5-1$
$\Rightarrow-8\text{x}=4$
Dividing by -8,
$\frac{-8\text{x}}{-8}=\frac{4}{-8}$
$\Rightarrow\text{x}=\frac{1}{-2}$
$\therefore\text{x}=\frac{-1}{2}$
Verification:
$\text{L.H.S.}=\frac{2\text{x}-1}{3}-\frac{6\text{x}-2}{5}$
$=\frac{2\Big(\frac{-1}{2}\Big)-1}{3}-\frac{6\Big(\frac{-1}{2}\Big)-2}{5}$
$=\frac{-1-1}{3}-\frac{-3-2}{5}$
$=\frac{-2}{3}-\frac{-5}{5}=\frac{-2}{3}+1$
$=\frac{1}{3}=\text{R.H.S.}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Look at the measures shown in the given figure and find the area of ☐PQRS.
In the following table, data of the transport means used by students in 8th standard for commutation between home and school is given. Draw a subdivided bar diagram to show the data.
(Scale: On Y axis: 1 cm = 500 students)
(Scale: On Y axis: 1 cm = 500 students)
| Means of commutation\Town | Paithan | Yeola | Shahapur |
| Cycle | 3250 | 1500 | 1250 |
| Bus and auto | 750 | 500 | 500 |
| On foot | 1000 | 1000 | 500 |
A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a beggar waiting outside the shop. She spent half of what was left on a lunch and followed that up with a two rupee tip. She spent half of the remaining amount on a book and three rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?
Draw a line l. Take a point T outside the line. Through point T draw a line parallel to line l.
Construct a quadrilateral ABCD in which AB = 4cm, AC = 5cm, AD = 5.5cm and $\angle\text{ABC}=\angle\text{ACD}=90^\circ.$
→It x and y vary inversely, fill in the following blanks:
|
x
|
12
|
16
|
...
|
8
|
...
|
|
y
|
...
|
6
|
4
|
...
|
0.25
|
Observe the following graph and answer the questions.
- State the type of the bar graph.
- How much percent is the Tur production to total production in Ajita’s farm?
- Compare the production of Gram in the farms of Yash and Ravi and state whose percentage of production is more and by how much?
- Whose percentage production of Tur is the least?
- State production percentages of Tur and Gram in Sudha’s farm.
Draw an acute angled ∆PQR. Draw all of its altitudes. Name the point of concurrence as ‘O’.
Construct a frequency table for the following weights (in gm) of 35 mangoes using the equal class intervals, one of them is 40-50 (45 not included):
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.
30, 40, 45, 32, 43, 50, 55, 62, 70, 70, 61, 62, 53, 52, 50, 42, 35, 37, 53, 55, 65, 70, 73, 74, 45, 46, 58, 59, 60, 62, 74, 34, 35, 70, 68.
- What is the class mark of the class interval 40-45?
- What is the range of the above weights?
- How many classes are there?
Construct a quadrilateral ABCD, where AB = 4.2cm, BC = 3.6cm, CD = 4.8cm, $\angle\text{B}=30^\circ$ and $\angle\text{C}=150^\circ.$
→